00:01
Hi there, so for this problem we need to prove that for an ideal gas the coefficient of volume expansion is given by the following.
00:08
Okay, so the coefficient of volume expansion is 1 divided by the temperature.
00:12
Okay, so let's determine that first.
00:15
Okay, first of all we know that the coefficient of volume expansion as it states is related to the change in the volume.
00:23
So the change in the volume is the coefficient and times the initial volume, this times the temperature, the change in the temperature, okay? now, let's move things around and solve for the coefficient beta.
00:38
So then in here, we just move everything to the left side.
00:44
So we obtain 1 divided by the initial volume, v0, times the change in the volume divided by the change in temperature.
00:51
You can recognize in here this term is just simply the partial derivative of the volume with respect to the temperature.
01:00
This, of course, leaving the pressure as constant.
01:04
So let's write it in that way.
01:10
Okay, once we have this, we know that for an ideal gas, we know that there is a relationship between the pressure, the volume, and the temperature.
01:27
So the pressure between the pressure and volume is equal to the number of moles times the gas constant times the temperature...